FRANKFURT, April 30 (Reuters) - Deutsche Telekom CEO Tim Hoettges expressed confidence on Monday that the $26 billion takeover of Sprint Corp by its U.S. unit T-Mobile US would clear anti-trust hurdles.

Hoettges, speaking after the deal was announced on Sunday, underlined that it would enable Telekom to vote on behalf of Sprint's main owner, Japan's Softbank, thus securing overall control of the No.3 U.S. wireless player.

It was third time lucky after Softbank CEO Masayoshi Son first floated the idea of a merger only to be discouraged by the Obama administration. Talks on a deal fell apart over the issue of control last November.

"I have been working on this deal for 7 years," Hoettges told analysts on a call. "We have never been so optimistic as we have been today."

Under the all-share transaction, which will create a company with 127 million customers that rivals market leaders Verizon Communications and AT&T Inc, Deutsche Telekom would have a 42 percent stake and Softbank 27 percent.

But the German company will, as part of a proxy agreement, be able to vote for Softbank's shares, giving it effective control over 69 percent of the merged T-Mobile - and enabling it to consolidate its results. Both sides have agreed to hold on to their shares for four years.

The relative underperformance of Sprint's shares since the collapse of talks last autumn changed the equation in Deutsche Telekom's favour, making it possible to create a cleaner governance structure.

"This gives us the clear capability of steering the company in a clear and focused way," Hoettges said, describing the arrangement as a vote of confidence on the part of 'Masa San', the Softbank CEO.

Deutsche Telekom's shares opened 3 percent higher as analysts added synergies estimated by the parties to the deal at $43 billion into their valuations and some upgraded their recommendations on the stock. They later fell back to trade up 1.5 percent at 14.76 euros.

Jefferies estimated the deal upside at 2.40 euros per share for Deutsche Telekom, assuming flawless execution. Based on its weighted analysis of the deal's chances of happening as planned, it put the upside at 60 euro cents, or 4 percent.

The deal, which will involve refinancing Sprint's heavy debt load, would push Deutsche Telekom's net leverage out of its target corridor of 2.0-2.5 times core earnings, but this should return to the comfort zone by 2021, the company said.

Ratings agency S&P said it was putting Deutsche Telekom's BBB+ rating under review for a possible downgrade, however, estimating the deal would push its leverage ratio to 3.6-3.9 times in 2019 assuming it closes as planned.

SYNERGY BONANZA

The takeover would create huge cost synergies, worth an annual $6 billion, that Hoettges said would boost Deutsche Telekom's earnings per share within three years.

Most of those savings will come from eliminating duplication in network infrastructure as the merged entity frees up cash to invest in fifth-generation (5G) services that would, for example, help connect devices across the industrial internet.

Yet it will face close scrutiny from the U.S. authorities starting with the Department of Justice (DoJ) and the Federal Communications Commission (FCC).

Other steps include a national security review by the Committee on Foreign Investment in the United States (CFIUS), the U.S. federal states, and President Donald Trump's White House.

"Remedies remain a major imponderable," Bernstein analyst Dhananjay Mirchandani said in a note. "This deal has been announced, but is by no means done. Mid-2019 is likely the earliest we will know."

Hoettges was nonetheless bullish on prospects for approval: "It's good for America and good for its consumers if we do this transaction," he told reporters.

Rather than looking at the proposed combination of T-Mobile and Sprint as deal between wireless operators, regulators should take a broader view that takes account of fixed line players in an increasingly 'converged' market.

The transaction, which would create a business far bigger than Deutsche Telekom's core German business, was broadly self-funding and would not have a direct impact on strategy or jobs in the European markets where it is present.

But it would, in creating 5G momentum, set an example to Europe which is lagging the rest of the world, said Hoettges, noting that network operators can buy radio spectrum in the United States but only rent it in Europe.

"The U.S. system is more successful than the European one," he said. (Reporting by Edward Taylor and Douglas Busvine Editing by Keith Weir/Adrian Croft)